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jeyben [28]
3 years ago
5

Assume that the GMAT scores across the U.S. follow a bell shaped distribution (symmetric and unimodal) with mean 549 and standar

d deviation 76. Use the Empirical Rule (68-95-99.7 rule) to answer the following question: What is the GMAT score corresponding to the 16th percentile
Mathematics
1 answer:
blondinia [14]3 years ago
5 0

Answer:

The GMAT score corresponding to the 16th percentile is 473.

Step-by-step explanation:

Empirical Rule.

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

68% of the measures within 1 standard deviation of the mean.

This means that they are between the 50 - (68/2) = 50 - 34 = 16th percentile(one standard deviation below the mean) and the 50 + (68/2) = 50 + 34 = 84th percentile(one standard deviation above the mean).

In this question:

Mean of 549, standard deviation of 76.

16th percentile:

One standard deviation below the mean, so 549 - 76 = 473.

The GMAT score corresponding to the 16th percentile is 473.

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2 years ago
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Please help me in this questions....​
Ivahew [28]

Part (i)

I'm going to use the notation T(n) instead of T_n

To find the first term, we plug in n = 1

T(n) = 2 - 3n

T(1) = 2 - 3(1)

T(1) = -1

The first term is -1

Repeat for n = 2 to find the second term

T(n) = 2 - 3n

T(2) = 2 - 3(2)

T(2) = -4

The second term is -4

<h3>Answers: -1, -4</h3>

==============================================

Part (ii)

Plug in T(n) = -61 and solve for n

T(n) = 2 - 3n

-61 = 2 - 3n

-61-2 = -3n

-63 = -3n

-3n = -63

n = -63/(-3)

n = 21

Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).

<h3>Answer:  21st term</h3>

===============================================

Part (iii)

We're given that T(n) = 2 - 3n

Let's compute T(2n). We do so by replacing every copy of n with 2n like so

T(n) = 2 - 3n

T(2n) = 2 - 3(2n)

T(2n) = 2 - 6n

Now subtract T(2n) from T(n)

T(n) - T(2n) = (2-3n) - (2-6n)

T(n) - T(2n) = 2-3n - 2+6n

T(n) - T(2n) = 3n

Then set this equal to 24 and solve for n

T(n) - T(2n) = 24

3n = 24

n = 24/3

n = 8

This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.

<h3>Answer: 8</h3>
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3 years ago
Help please! One question! xoxo
AVprozaik [17]

Answer:

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Step-by-step explanation:

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3 years ago
Dave delivered 52 newspapers in all. saturday &amp; sunday. he delivered 8 more newspapers on sunday than on saturday. how many
mihalych1998 [28]
Sat + Sun = 52
Sun = Sat + 8

Sat + Sat + 8 = 52
2Sat + 8 = 52
2Sat + 8-8 = 52-8
2Sat = 44
2Sat/2 = 44/2
Sat = 22

Sun = 22 + 8
Sun = 30

Check
Sat + Sun = 52
22 + 30 = 52
52 = 52
6 0
3 years ago
Find the real numbers x and y that make the equation true. (2 points)<br> -3 + yi = x + 6i
stealth61 [152]

Answer:

x = - 3, y = 6

Step-by-step explanation:

For the 2 sides to be equal then the coefficients of the imaginary terms and the real terms must be equal.

Given

- 3 + yi = x + 6i , then

x = - 3 and y = 6

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